...I personally put up resource starbases whenever I have the opportunity but don't expect them to survive long when war breaks out.
...I don't actually have any significant 'house' though.

Resource starbases are universally used, of course.

Influence starbases are also used extensively if you are trying to assimilate another race (or just steal a few of their planets).

If I have a few good manufacturing or research planets that can be covered with multiple starbases, I will mass economic starbases there.

I almost never use military starbases - I can't get constructors to the front lines fast enough to keep the starbase from dying, and if I'm pushed back into my home territory that far I've lost anyway. They do make good outposts on Huge or Gigantic maps - especially with sensors, speed-affecting modules, and heavy defenses.

One strategy for an extended war on a very large map with an enemy far away would be to build a string of starbase 'highways' - build chains of military starbases with speed increasing (or decreasing, for enemies) modules to ferry your ships to the front lines rapidly. You can also equip every other one with sensors, defensive modules, and combat boosters in case things go south at the battlefront and you need to buy time for a retreat and regrouping.

You can also equip every other one with sensors, defensive modules, and combat boosters in case things go south at the battlefront and you need to buy time for a retreat and regrouping.

Wouldn't it be cheaper just to plop a fleet of tiny/small ships down on the same square as the starbase? You need a ton of constructors to get starbase attack/defense up to respectable levels and later on in the game, it's just going to die in a few shots anyway. Seems to me you could get the fleet for a similar or cheaper price than all those constructors and be able to move it to where it's needed.

Same thing with the sensors, 1 cargo ship loaded up with them would be a lot cheaper than all of the constructors you need to pump up the starbase sensors, and the cargo ship can move.

I sometimes use military starbases to make a strong point in my planetary defenses, but I never expect a starbase to hold an area on its own.

Now, when I'm REALLY bored, I'll put 16 military starbases in a sector corner and give them all both of the ship speed boosters, thus giving any ship that reaches the area the ability to "jump" an extra 32 parsecs to get something going in short order (usually an invasion or a defense redistribution). It's not efficient, but it can be amusing once in a while.